Entanglement generation through Markovian feed-back in open two-qubit systems

We discuss the generation and the long-time persistence of entanglement in open two-qubit systems whose reduced dissipative dynamics is not apriori engineered but is instead subjected to filtering and Markovian feedback. In particular, we analytically study 1.) whether the latter operations may enhance the environment capability of generating entanglement at short times and 2.) whether the generated entaglement survives in the long-time regime. We show that, in the case of particularly symmetric Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) it is possible to fully control the convex set of stationary states of the two-qubit reduced dynamics, therefore the asymptotic behaviour of any initial two-qubit state. We then study the impact of a suitable class of feed-back operations on the considered dynamics.